tag:blogger.com,1999:blog-19590240684938398172018-03-05T23:55:51.999-08:00MATHAMANIACIf people do not believe that maths is simple,
it is only because they do not realize how complicated life is.Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.comBlogger34125tag:blogger.com,1999:blog-1959024068493839817.post-81827260785451890612012-03-20T18:57:00.002-07:002012-03-20T18:57:34.462-07:00<a href="http://banksoalanspm.com/">http://banksoalanspm.com/</a>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-28167832325667423472012-03-18T08:26:00.003-07:002012-03-18T08:26:42.991-07:00How to Study Math: Learn From Your Errors<ins style="border: none; display: inline-table; height: 60px; margin: 0; padding: 0; position: relative; visibility: visible; width: 468px;"><ins id="aswift_2_anchor" style="border: none; display: block; height: 60px; margin: 0; padding: 0; position: relative; visibility: visible; width: 468px;"></ins></ins> <br /><span style="font-size: 100%; font-weight: bold;"><img alt="finger-in-socket-1" class="alignleft size-medium wp-image-73" height="162" src="http://www.holmezideas.com/wp-content/uploads/2009/09/finger-in-socket-1-300x225.jpg" title="finger-in-socket-1" width="216" /> This is probably one of the more important sections here and also one of the most over looked. Learning from your mistakes can only help you.</span><br /> <span style="font-size: 100%;"><span style="font-weight: bold;">Review Homework</span>. When you get your homework back review it looking for errors that you made.</span><span style="font-size: 100%;"><span style="font-weight: bold;">Review Exams</span>. Do the same thing with exams.</span><br /><span style="font-size: 100%;">Understand the Error. When you find an error in your homework or exams try to understand what the error is and just what you did wrong. Look for something about the error that you can remember to help you to avoid making it again.</span><span style="font-size: 100%;"><span style="font-weight: bold;">Get Help</span>. If you can find the error and/or don’t understand why it was an error then get help. Ask the instructor, your tutor, or a classmate who got the problem correct.</span><br /> <span style="font-size: 100%;"><span style="font-weight: bold;">Rushed Errors</span>.</span><span style="font-size: 100%;"> If you find yourself continually making silly arithmetic or notational errors then slow down when you are working the problems. Most of these types of errors happen because students get in a hurry and don’t pay attention to what they are doing.</span><br /> <span style="font-size: 100%;"><span style="font-weight: bold;">Repeated Errors</span>. If you find yourself continually making errors on one particular type of problem then you probably don’t have a really good grasp of the concept behind that type of problem. Go back and find more examples and really try to understand just what you are doing wrong or don’t understand.</span><br /> <span style="font-size: 100%;"><span style="font-weight: bold;">Keep a List of Errors</span>. Put errors that you keep making in a “list of errors”. With each error write down the correct method/solution. Review the list after you complete a problem and see if you’ve made any of your “common” error</span>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-43394266348525078622012-03-18T08:25:00.002-07:002012-03-18T08:25:11.069-07:00The Calculator<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-C25_Zl8d42U/T2X0xCvzviI/AAAAAAAAAEw/NWZKUUzK9YE/s1600/My+Calculator.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/-C25_Zl8d42U/T2X0xCvzviI/AAAAAAAAAEw/NWZKUUzK9YE/s320/My+Calculator.jpg" width="320" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-41498505031255897582012-03-18T07:43:00.001-07:002012-03-18T07:43:23.146-07:00Maths Pic<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-dyxcZoNj_6k/T2X0Y73odfI/AAAAAAAAAEo/NgFizpU0yqY/s1600/maths.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://3.bp.blogspot.com/-dyxcZoNj_6k/T2X0Y73odfI/AAAAAAAAAEo/NgFizpU0yqY/s320/maths.jpg" width="320" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-78309232466459378392012-03-18T07:37:00.001-07:002012-03-18T07:37:16.585-07:00Math(S)<div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/gsWKyFg9IdM?feature=player_embedded' FRAMEBORDER='0' /></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-19173853242074246952012-03-18T07:32:00.004-07:002012-03-18T07:32:44.646-07:00Maths Song<div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/obIGsb-IZMo?feature=player_embedded' FRAMEBORDER='0' /></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-2478987104379474922012-03-18T07:29:00.003-07:002012-03-18T07:29:28.771-07:00Introduction to Algebra<table align="center" border="0" style="width: 250px;"> <tbody><tr valign="middle"> <td align="center" class="largemono" width="50"> <b><span style="font-size: x-large;"><i>x</i></span></b></td> <td align="center" class="largemono" width="50"> <b><span style="font-size: x-large;">+</span></b></td> <td align="center" class="largemono" width="50"> <b><span style="font-size: x-large;">5</span></b></td> <td align="center" class="largemono" width="50"> <b><span style="font-size: x-large;">=</span></b></td> <td align="center" class="largemono" width="50"> <b><span style="font-size: x-large;">12</span></b></td> </tr></tbody></table><br /> <div class="simple"> <table align="center" border="0"> <tbody><tr> <td width="400">Start with:</td> <td align="center" class="larger" width="180">x + 5 = 12</td> </tr><tr> <td>&nbsp;</td> <td>&nbsp;</td> </tr><tr> <td> What you are aiming for is an answer like "x = ...", and the <i>plus 5</i> is in the way of that!<br /> If you <i>subtract 5</i> you can cancel out the <i>plus 5</i> (because 5-5=0)<br /> </td> <td align="center" class="larger">&nbsp;</td> </tr><tr> <td>&nbsp;</td> <td align="center" class="larger">&nbsp;</td> </tr><tr> <td>So, let us have a go at subtracting 5 from <b>both sides</b>:</td> <td align="center" class="larger">x+5 <b>-5</b> = 12 <b>-5</b></td> </tr><tr> <td>&nbsp;</td> <td align="center" class="larger">&nbsp;</td> </tr><tr> <td>A little arithmetic (5-5 = 0 and 12-5 = 7) becomes:</td> <td align="center" class="larger">x+0 = 7</td> </tr><tr> <td>&nbsp;</td> <td align="center" class="larger">&nbsp;</td> </tr><tr> <td>Which is just:</td> <td align="center" class="larger"><b>x = 7</b></td> </tr><tr> <td>&nbsp;</td> <td align="center" class="larger"><b><i>Solved!</i></b></td> </tr><tr> <td>(Quick Check: 7+5=12)</td> <td align="center" class="larger">&nbsp;</td> </tr></tbody></table></div>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-12329051545749348332012-03-18T07:23:00.001-07:002012-03-18T07:23:06.205-07:00Ships<br /> <img alt="Ships" height="118" src="http://www.mathsisfun.com/puzzles/images/einstein.gif" style="float: left; margin-bottom: 10px; margin-right: 10px;" width="91" /><b>The Puzzle:</b> There are 5 ships in a port:<br /><br /> 1. The Greek ship leaves at six and carries coffee.<br /> 2. The Ship in the middle has a black chimney.<br /> 3. The English ship leaves at nine.<br /> 4. The French ship with blue chimney is to the left of a ship that carries coffee.<br /> 5. To the right of the ship carrying cocoa is a ship going to Marseille.<br /> 6. The Brazilian ship is heading for Manila.<br /> 7. Next to the ship carrying rice is a ship with a green chimney.<br /> 8. A ship going to Genoa leaves at five.<br /> 9. The Spanish ship leaves at seven and is to the right of the ship going to Marseille.<br /> 10. The ship with a red chimney goes to Hamburg.<br /> 11. Next to the ship leaving at seven is a ship with a white chimney.<br /> 12. The ship on the border carries corn.<br /> 13. The ship with a black chimney leaves at eight.<br /> 14. The ship carrying corn is anchored next to the ship carrying rice.<br /> 15. The ship to Hamburg leaves at six.<br /><br />Which ship goes to Port Said? Which ship carries tea?<br /><br /><h2>The Solution . . .</h2><table align="center" border="0" style="width: 580px;"><tbody><tr> <td class="Larger">The Spanish ship goes to Port Said and the French ship carries tea. However, tea can be carried by the Brazilian ship, too.<br /><br />If you understood position 'to the right' to mean anywhere on the right side from the given point (not only right next to).<br /><br /><table border="1" cellpadding="3" cellspacing="0"><tbody><tr><td>French</td><td>5.00</td><td>tea</td><td>blue</td><td>Genoa</td></tr><tr><td>Greek</td><td>6.00</td><td>coffee</td><td>red</td><td>Hamburg</td></tr><tr><td>Brazilian</td><td>8.00</td><td>cocoa</td><td>black</td><td>Manila</td></tr><tr><td>English</td><td>9.00</td><td>rice</td><td>white</td><td>Marseille</td></tr><tr><td>Spanish</td><td>7.00</td><td>corn</td><td>green</td><td>Port Said</td></tr></tbody></table></td></tr></tbody></table>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-23129887036087565572012-03-18T07:15:00.001-07:002012-03-18T07:19:55.639-07:00A Level<div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/h3wdStMSfXk?feature=player_embedded' FRAMEBORDER='0' /></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-30322214972670816552012-03-18T07:12:00.000-07:002012-03-18T07:12:03.044-07:00Wasan geometry<h5><em></em></h5><table align="center" class="pictable"> <tbody><tr> <td width="50"></td> <td><img alt="pic" height="100" src="http://hermay.org/jconstant/wasan/images-slimbox/bk2.jpg" width="100" /></td> <td width="50"></td> </tr><tr> <td width="50">&nbsp;</td> <td>&nbsp;</td> <td width="50">&nbsp;</td> </tr></tbody></table><div align="left"> <div class="text"><em>&nbsp;&nbsp;&nbsp; "</em>Wasan" geometry or traditional Japanese mathematics flourished under the Tokugawa shogunate around the Edo period and expressed itself in a unique way through mathematical votive pictures called San Gaku, written in formal Sino-Japanese language and displayed in temples and public places.<br /> Beautiful wooden tablets of many sizes and shapes would outline in pleasant and colorful way mathematical problems mostly left for the viewer to solve. This tradition slowly disappeared and today less than a thousand Sangaku have survived abandon or destruction. </div><div class="text">&nbsp;&nbsp;<em> In Dr. <a href="http://www.amazon.com/Japanese-Temple-Geometry-Problems-Sangaku/dp/0919611214">Fukagawa</a> and <a href="http://links.jstor.org/sici?sici=0002-9890%28199104%2998%3A4%3C381%3AJTGP%3E2.0.CO;2-F">D. Pedoe </a>own words:</em></div><div class="text">&nbsp;&nbsp; <em>During the greater part of the Edo period (1603-1867) Japan was almost completely cut off from the western world. Books on mathematics, if they entered Japan at all, must have been scarce, and yet, during this long period of isolation people of all social classes, from farmers to samurai, produced theorems in Euclidean geometry which are remarkably different from those produced in the west during the centuries of schism, and sometimes anticipated these theorems by many years..<br /> &nbsp;&nbsp;&nbsp; These theorems were not published in books, but appeared as beautifully coloured drawings on wooden tablets which were hung under the roof in the precincts of a shrine or temple.</em></div><div class="text"><br /></div></div><table align="center" class="pictable"> <tbody><tr> <td width="50"></td> <td><img alt="pic" height="30" src="http://hermay.org/jconstant/wasan/visuals/insert2.jpg" width="100" /></td> <td width="50"></td> </tr><tr> <td width="50">&nbsp;</td> <td>&nbsp;</td> <td width="50">&nbsp;</td> </tr></tbody></table><div align="justify"> <div class="text">&nbsp;&nbsp;&nbsp;&nbsp;The following is an extended series of variations on Sangaku problems - a tribute to mathematicians and artists alike who graced the walls of many temples in eighteenth century Japan. This work would not have been made possible without the interest and dedication of mathematicians Dr. <a href="http://www.amazon.com/Japanese-Temple-Geometry-Problems-Sangaku/dp/0919611214">Fukagawa</a>, <a href="http://links.jstor.org/sici?sici=0002-9890%28199104%2998%3A4%3C381%3AJTGP%3E2.0.CO%3B2-F">Pedoe</a>, <a href="http://www.princeton.edu/main/news/archive/S15/04/04O77/index.xml?section=topstories">Rothman</a>, <a href="http://www.wasan.jp/">Kotera</a> and the many other who provided inspiration, guidance and support throughout this adventure. </div><div class="text"><em>The artworks featured in the galleries are printed 20'x20', 220g., archival fine art paper. and available for purchase, individually or in series. Contact the artist for more information. </em></div></div>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com1tag:blogger.com,1999:blog-1959024068493839817.post-82532727314142703002012-03-18T06:33:00.002-07:002012-03-18T06:33:45.307-07:00Math in SmartphoneAre you bored of doing the same math question with the same method of doing it.?Well lets join us and play Math Maniac.Math Maniac is a very fun and addictive game.You can find this app on your smartphone.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Oo6K_VAHsjw/T2Xel8DythI/AAAAAAAAAEQ/VWMur1Wxsbw/s1600/mathmaniac.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="156" src="http://2.bp.blogspot.com/-Oo6K_VAHsjw/T2Xel8DythI/AAAAAAAAAEQ/VWMur1Wxsbw/s320/mathmaniac.jpg" width="320" /></a></div><div class="" style="clear: both; text-align: center;">The goal of Math Maniac is simple.In 10 seconds,player have to combine numbers to equal the number at in the left bottom corner.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Lwj8HcUyLtU/T2XetHi_BPI/AAAAAAAAAEY/ozKE53mgWzM/s1600/13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-Lwj8HcUyLtU/T2XetHi_BPI/AAAAAAAAAEY/ozKE53mgWzM/s1600/13.jpg" /></a><a href="http://3.bp.blogspot.com/-cO5wR5tHNxw/T2XevQYGntI/AAAAAAAAAEg/JwAWdF8vaC4/s1600/14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-cO5wR5tHNxw/T2XevQYGntI/AAAAAAAAAEg/JwAWdF8vaC4/s1600/14.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;">Hope this app will help you think that math is not just in your test paper but also in your communication device.</div><br /><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-6001852394291829582012-03-18T05:48:00.000-07:002012-03-18T05:48:44.078-07:00Just having fun<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-frbVXJEfz-k/T2XY447eTSI/AAAAAAAAAEI/8TBv8P7wJz8/s1600/i+love.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-frbVXJEfz-k/T2XY447eTSI/AAAAAAAAAEI/8TBv8P7wJz8/s320/i+love.JPG" width="213" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-39618504436882905972012-03-18T03:47:00.001-07:002012-03-18T03:47:23.482-07:00Creative Thinking<div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/otCLgQjBaio?feature=player_embedded' FRAMEBORDER='0' /></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-47558122705201580822012-03-18T03:42:00.002-07:002012-03-18T03:42:31.851-07:00Hahahaha<div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/UDHxgsNqtBA?feature=player_embedded' FRAMEBORDER='0' /></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-22762954441667078162012-03-17T20:43:00.001-07:002012-03-17T20:43:18.043-07:00Kirigami and MathematicsKirigami is an art which is a combination of origami i.e. paper folding and paper cutting.In Japan the word Kirigami has been in use for a long time because "kiru" means to cut and "gami" means paper.Making paper snowflakes is an example of Kirigami.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-MKskVUfsStw/T2VXC44HL_I/AAAAAAAAADw/LUONrxffAPM/s1600/kirigami.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-MKskVUfsStw/T2VXC44HL_I/AAAAAAAAADw/LUONrxffAPM/s1600/kirigami.jpg" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-zH3_DjrEW3E/T2VXKptL5XI/AAAAAAAAAD4/HqLKIxz6zak/s1600/kirimagi2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-zH3_DjrEW3E/T2VXKptL5XI/AAAAAAAAAD4/HqLKIxz6zak/s1600/kirimagi2.jpg" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-Mhr1R2_lGEc/T2VXMHVNTxI/AAAAAAAAAEA/PHmrrOoOZ3Y/s1600/kirigami3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Mhr1R2_lGEc/T2VXMHVNTxI/AAAAAAAAAEA/PHmrrOoOZ3Y/s1600/kirigami3.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">You can explore many hidden symmetry patterns and write on mathematical interpretations.This way we would not only start loving mathematics but surely ask for more of it.</div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-85762048894704236892012-03-17T20:18:00.000-07:002012-03-17T20:18:07.272-07:00Fibonacci SequenceIt was first observed by the Italian mathematician Leonardo Fibonacci in 1202<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-VsRS_hS7w8A/T2VOoamMu9I/AAAAAAAAADg/U1Wgir_Rf1E/s1600/fibonacci.jpg" imageanchor="1" style="display: inline !important; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://2.bp.blogspot.com/-VsRS_hS7w8A/T2VOoamMu9I/AAAAAAAAADg/U1Wgir_Rf1E/s1600/fibonacci.jpg" /></a></div><div class="separator" style="clear: both; text-align: left;">He was investigating how fast rabbits could breed under ideal circumstances.He made the following assumptions:</div><div class="separator" style="clear: both; text-align: left;">Begin with one male and one female rabbits.Rabbits can mate at the age of one month,so by the end of the second month,each female can produce another pair of rabbits.The rabbits never die.The female produce one male and one female every month.He calculate how many pair of rabbits would be produce in one year.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div style="text-align: center;">&nbsp;<a href="http://3.bp.blogspot.com/-cPIHR4ZbcAs/T2VOq5R5xTI/AAAAAAAAADo/2Szm-D-Mg5Q/s1600/flower.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-cPIHR4ZbcAs/T2VOq5R5xTI/AAAAAAAAADo/2Szm-D-Mg5Q/s1600/flower.jpg" /></a></div><div style="text-align: center;">This flower is one of the art of Fibonacci...</div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-12284882564991061062012-03-17T07:35:00.002-07:002012-03-18T03:27:54.581-07:00Quadratic Equations<h2 style="color: yellow;"> <b>3 Basic Techniques in Solving Quadratic Equation Questions</b></h2>In this chapter we will learn 3 most basic techniques on how to:<br /><ol><b><li>Solve the quadratic equations</li><li>Form a quadratic equation</li><li>Determine the conditions for the type of roots.</li></b><b></b></ol><span id="more-240"></span><br />Generally, <img alt="{{x}^{2}}-6x+5=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D-6x%2B5%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}-6x+5=0" /> is the quadratic equation, expressed in the general form of <img alt="a{{x}^{2}}+bx+c=0" class="latex" src="http://s0.wp.com/latex.php?latex=a%7B%7Bx%7D%5E%7B2%7D%7D%2Bbx%2Bc%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="a{{x}^{2}}+bx+c=0" />, where a=1, b=- 6 and c=5. &nbsp;The <b>root</b> is the value of x that can solve the equations.<br /><blockquote class="tr_bq">&nbsp;quadratic equation only has <b>two roots</b>.</blockquote><br /><b><i>Example1</i></b><i>: What are the roots of <img alt="{{x}^{2}}-6x+5=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D-6x%2B5%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}-6x+5=0" /><i></i>?<br />Answer: The value of 1 and 5 are the roots of the quadratic equation, because you will get zero when substitute 1 or 5 in the equation. We will further discuss on how to solve the quadratic equation<span style="color: cyan;"> and </span><span style="color: black;">find out the roots later.</span></i><br /><h3 style="color: lime;"> <b>1)&nbsp;&nbsp;&nbsp;&nbsp; </b><b>Solve the quadratic equations</b></h3>There are many ways we can use to solve quadratic equations such as using:<br />1)&nbsp;&nbsp;&nbsp;&nbsp; substitution,<br />2)&nbsp;&nbsp;&nbsp;&nbsp; inspection,<br />3)&nbsp;&nbsp;&nbsp;&nbsp; trial and improvement method,<br />4)&nbsp;&nbsp;&nbsp;&nbsp; factorization,<br />5)&nbsp;&nbsp;&nbsp;&nbsp; completing the square and<br />6)&nbsp;&nbsp;&nbsp;&nbsp; Quadratic formula.<br />However, we will only focus on the last three methods as there are the most commonly use methods to solve a quadratic equation in the SPM questions. Let’s move on!<br /><h4 style="color: lime;"> <b>Factorization</b></h4>Factorization is the decomposition of a number into the product of the other numbers, example, 12 could be factored into 3 x 4, 2 x 6, and 1 x 12.<br /><b><i>Example 2</i></b><i>: Solve &nbsp;<img alt="{{x}^{2}}+7x+12=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D%2B7x%2B12%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}+7x+12=0" /> using factorization.<br />Answer: We can factor the number 12 into 4 x 3. Remember, always think of the factors which can be added up to the get the middle value (3+4 = 7), refer factorization table below, </i><br /><a href="http://perfectmaths.files.wordpress.com/2011/07/factorization-table1.png"><img alt="factorization table" class="alignnone size-full wp-image-253" src="http://perfectmaths.files.wordpress.com/2011/07/factorization-table1.png?w=604" title="factorization table" /></a><br />So we will get ( x + 3 )( x + 4 ) = 0,<br />x + 3 = 0&nbsp;&nbsp;&nbsp; or&nbsp;&nbsp; x + 4 = 0<br />x = – 3&nbsp; or&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x&nbsp; = – 4<br /><b><i>Example 3</i></b><i>: Solve&nbsp;</i><img alt="10x-3=8x^2" class="latex" src="http://s0.wp.com/latex.php?latex=10x-3%3D8x%5E2&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="10x-3=8x^2" />&nbsp;<i>using factorization.<br />Answer: Rearrange the equation in the form of&nbsp;</i><img alt="a{{x}^{2}}+bx+c=0" class="latex" src="http://s0.wp.com/latex.php?latex=a%7B%7Bx%7D%5E%7B2%7D%7D%2Bbx%2Bc%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="a{{x}^{2}}+bx+c=0" /><br /><a href="http://perfectmaths.files.wordpress.com/2011/07/eg3-factorization.png"><img alt="" class="alignnone size-full wp-image-278" src="http://perfectmaths.files.wordpress.com/2011/07/eg3-factorization.png?w=604" title="eg3-factorization" /></a><br />So we will get (4x – 3)(2x – 1)=0,<br />4x – 3 = 0&nbsp;&nbsp;&nbsp; or&nbsp;&nbsp; 2x – 1 = 0<br />x = <img alt="\frac{3}{4}" class="latex" src="http://s0.wp.com/latex.php?latex=%5Cfrac%7B3%7D%7B4%7D&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\frac{3}{4}" />&nbsp;&nbsp;&nbsp;or&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x&nbsp; = <img alt="\frac{1}{2}" class="latex" src="http://s0.wp.com/latex.php?latex=%5Cfrac%7B1%7D%7B2%7D&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\frac{1}{2}" /><br /><h4> <span style="color: #003366;"><b><span style="color: lime;">Completing the square</span> </b></span></h4><b><i>Example 4</i></b><i>: Solve the following equation by using completing the square method.&nbsp;</i><br /><a href="http://perfectmaths.files.wordpress.com/2011/07/eg4-a.png"><img alt="example 4" class="alignnone size-full wp-image-280" src="http://perfectmaths.files.wordpress.com/2011/07/eg4-a.png?w=604" title="eg4-a" /></a><br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/eg4-b2.png"><img alt="example 4b" class="alignnone size-full wp-image-286" src="http://perfectmaths.files.wordpress.com/2011/07/eg4-b2.png?w=604" title="eg4-b" /></a><br /></i><br /><h4 style="color: lime;"> <b>Quadratic formula</b></h4><i><a href="http://perfectmaths.files.wordpress.com/2011/07/quadratic-formula.png"><img alt="Quadratic formula" class="alignnone size-full wp-image-284" src="http://perfectmaths.files.wordpress.com/2011/07/quadratic-formula.png?w=604" title="Quadratic formula" /></a></i><br />Normally when do you need to use this formula?<br />1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The exam question requested to do so!<br />2)&nbsp;&nbsp;&nbsp;&nbsp; The quadratic equation <b>cannot be factorized</b>.<br />3)&nbsp;&nbsp;&nbsp;&nbsp; The figure of a, b, and c of the equation <img alt="a{{x}^{2}}+bx+c=0" class="latex" src="http://s0.wp.com/latex.php?latex=a%7B%7Bx%7D%5E%7B2%7D%7D%2Bbx%2Bc%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="a{{x}^{2}}+bx+c=0" />&nbsp;are too <b>large</b> and <b>hard to factorized</b>.<br /><b><i>Example 5</i></b><i>: Solve <img alt="(x-2)=6x(x+3)" class="latex" src="http://s0.wp.com/latex.php?latex=%28x-2%29%3D6x%28x%2B3%29&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="(x-2)=6x(x+3)" />&nbsp; using quadratic formula.</i><br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/eg5-ans1.png"><img alt="example 5 answer" class="alignnone size-full wp-image-294" src="http://perfectmaths.files.wordpress.com/2011/07/eg5-ans1.png?w=604" title="eg5-ans" /></a></i><br /><h3 style="color: lime;"> <b>2)&nbsp;&nbsp;&nbsp;&nbsp; </b><b>Form a quadratic equation</b></h3>How do you form a quadratic equation if the roots of the equation are 1 and 2? Well, we can do the work out like this using the reverse method:<br />We can assume:<br />x = 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; or&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; x = 2<br />x – 1 = 0&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; or&nbsp;&nbsp;&nbsp;&nbsp; x – 2 = 0<br />(x-1)(x-2)=0<br />x<sup>2</sup>-2x-x+2=0<br />x<sup>2</sup>-3x+2=0<b></b><br />So the quadratic equation is <b>x<sup>2</sup> – 3x + 2=0</b>. This is the most basic technique to form up a quadratic equation.<br />Let’s assume we have the roots of <img alt="\alpha" class="latex" src="http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\alpha" />&nbsp;and <img alt="\beta" class="latex" src="http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\beta" />:<br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/forming-equation.png"><img alt="forming equation explanation" class="alignnone size-full wp-image-302" src="http://perfectmaths.files.wordpress.com/2011/07/forming-equation.png?w=604" title="forming equation" /></a></i><br />In other words, we can form up the equation using the sum of roots (SOR) and product of roots (POR). If the roots are 1 and 2,<br />SOR = 1+2<br />= 3<br />POR = 1 x 2<br />=2<br /><i><img alt="{{x}^{2}}-(\text{sum of roots)}x+(\text{product of roots)}=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D-%28%5Ctext%7Bsum+of+roots%29%7Dx%2B%28%5Ctext%7Bproduct+of+roots%29%7D%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}-(\text{sum of roots)}x+(\text{product of roots)}=0" /></i><br /><i><img alt="{{x}^{2}}-3x+2=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D-3x%2B2%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}-3x+2=0" /></i><br />Sometime we need to determine the SOR and POR from a given quadratic equation in order to find a new equation from a given new roots. In general form,<br /><a href="http://perfectmaths.files.wordpress.com/2011/07/forming-equation2.png"><img alt="forming equation explanation2" class="alignnone size-full wp-image-303" src="http://perfectmaths.files.wordpress.com/2011/07/forming-equation2.png?w=604" title="forming equation2" /></a><br />Let’s look at the example below on how the concept above can help us solve the question.<br /><b><i>Example 6:</i></b><i> Given that <img alt="\alpha" class="latex" src="http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\alpha" />&nbsp;and <img alt="\beta" class="latex" src="http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\beta" /> are the roots of <img alt="5{{x}^{2}}-2x-2=0" class="latex" src="http://s0.wp.com/latex.php?latex=5%7B%7Bx%7D%5E%7B2%7D%7D-2x-2%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="5{{x}^{2}}-2x-2=0" /> , form a quadratic equation <img alt="a{{x}^{2}}+bx+c=0" class="latex" src="http://s0.wp.com/latex.php?latex=a%7B%7Bx%7D%5E%7B2%7D%7D%2Bbx%2Bc%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="a{{x}^{2}}+bx+c=0" />&nbsp;with the roots of (<i><img alt="\alpha" class="latex" src="http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\alpha" />&nbsp;</i>- 5 ) and ( <i><img alt="\beta" class="latex" src="http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="\beta" />&nbsp;</i>- 5 ).&nbsp;</i><br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part11.png"><img alt="example 6 answer part1" class="alignnone size-full wp-image-313" src="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part11.png?w=604" title="eg6 ans part1" /></a><a href="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part1.png"><br /></a><a href="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part2.png"><img alt="example 6 ans part2" class="alignnone size-full wp-image-306" src="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part2.png?w=604" title="eg6 ans part2" /></a></i><br /><h3 style="color: lime;"> <b>3)&nbsp;&nbsp;&nbsp;&nbsp; </b><b>Determine the conditions for the type of roots</b></h3>Refer back to example 2, we know that <img alt="{{x}^{2}}+7x+12=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D%2B7x%2B12%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}+7x+12=0" />&nbsp;<i></i>has two different roots (-3 and -4) by solving using factorization method. However, how are we going to determine the types of roots of <img alt="{{x}^{2}}+7x+12=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D%2B7x%2B12%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}+7x+12=0" /><i></i>&nbsp;without solving the equation? The trick is we can use <img alt="{{b}^{2}}-4ac" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bb%7D%5E%7B2%7D%7D-4ac&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{b}^{2}}-4ac" /><i></i>.<br /><i></i><img alt="{{b}^{2}}-4ac" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bb%7D%5E%7B2%7D%7D-4ac&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{b}^{2}}-4ac" />&nbsp;is called a discriminant. Remember, when the value is greater than 0, we have 2 different roots, when it is 0, we have 2 equal roots, and when it is less than 0, we have no roots.<br />From the quadratic equation, <img alt="{{x}^{2}}+7x+12=0" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D%2B7x%2B12%3D0&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}+7x+12=0" />&nbsp;, <img alt="a=1,b=7,c=12,\text{ so }{{7}^{2}}-4(1)(12)=1" class="latex" src="http://s0.wp.com/latex.php?latex=a%3D1%2Cb%3D7%2Cc%3D12%2C%5Ctext%7B+so+%7D%7B%7B7%7D%5E%7B2%7D%7D-4%281%29%2812%29%3D1&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="a=1,b=7,c=12,\text{ so }{{7}^{2}}-4(1)(12)=1" />&nbsp;, we have <b>2 different roots</b> since the discriminant is greater than zero. Refer table below.&nbsp;<i><a href="http://perfectmaths.files.wordpress.com/2011/07/eg6-ans-part2.png"><br /></a></i><br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/discriminant-table.png"><img alt="discriminant table" class="alignnone size-full wp-image-307" src="http://perfectmaths.files.wordpress.com/2011/07/discriminant-table.png?w=604" title="discriminant table" /></a></i><br /><b><i>Example 7:</i></b><i> A quadratic equation <img alt="{{x}^{2}}+2hx+4=x" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bx%7D%5E%7B2%7D%7D%2B2hx%2B4%3Dx&amp;bg=ffffff&amp;fg=4e4e4e&amp;s=0" title="{{x}^{2}}+2hx+4=x" />&nbsp;has two equal roots. Find the possible values of h.</i><br /><i><a href="http://perfectmaths.files.wordpress.com/2011/07/eg7-answer.png"><img alt="example 7 answer" class="alignnone size-full wp-image-311" src="http://perfectmaths.files.wordpress.com/2011/07/eg7-answer.png?w=604" title="eg7 answer" /></a></i>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-54002117968725685752012-03-17T07:08:00.003-07:002012-03-17T07:08:44.367-07:00SPM Modern Maths Tips<span style="font-weight: bold;">Brief Introduction</span><br />Mathematics (is also known as Modern Maths) and Additional Mathematics are categorized as thinking subjects which you take your time thinking rather than memorizing facts. The formula will be given at the front page of the examination paper. Additional Maths is notably 4 times harder than Modern Maths. It’s like if students think Maths is shit, then take Add Maths. If you get 90% marks in Maths, you may have potential to get 40% marks in Add Maths. It’s near to impossible for someone who get A1 in Add Maths fail in Math. Well it’s not important. What I’m going to discuss at here is Mathematics.<br /><br /><span style="font-weight: bold;">SPM Mathematics</span><br />In SPM, mathematics is considered as compulsory subject. You must pass this subject in order to get the certificates along with Malay language. Malay language test takes a lot of time and your hand hurts like hell after writing so many words. It’s not simple either. However, the percentage of students fail in Mathematics is higher than Malay Language in real SPM, which is ridiculous. It is told that Mathematics is quite ‘difficult’ among Art students in seminar SPM, which I can't believe my eyes either.<span class="fullpost"><br /><br />In my opinion, Mathematics is the easiest subject in SPM for Science students. I believe PMR students can even do with their PMR standard knowledge because some questions like volume of solid and area and perimeter of a circle being test in SPM. It’s not being taught in SPM therefore you can only depend on your past knowledge in Form 2. Although the questions are a lot easier than Add Maths, There are still some pupils having difficulties in Maths.<br /><br />I see some students leave the 'haven't done' answers after they get the formulae to be applied in the questions, which they didn’t really answer the questions. Some of them don’t understand the questions’ needs. Therefore, exercises and guidance from teachers are essential for improvement.<br /><br /><img alt="SPM Intervention KL 2008" border="0" id="BLOGGER_PHOTO_ID_5216870964345928866" src="http://4.bp.blogspot.com/_oGPceNeg9DA/SGYMgHzjfKI/AAAAAAAAAOY/WXt0fLSFSU8/s200/SPM+Intervention+2008.JPG" style="cursor: hand; cursor: pointer; float: right; margin: 0 0 10px 10px;" />The questions are so direct and mostly the answers will less likely to appear in decimal. You need a little bit of logic compare to Add maths. Besides that, even if you do well in monthly test, you might end up tilting head during SPM examination hall. It’s because monthly tests don’t follow the real format of SPM. Like Intervention 1 for KL state this year, there's no chance in hell this question is coming out in real SPM.<br /><br />Based on SPM Maths, it consists of 2 papers<br /><br /><span style="font-weight: bold;">Paper 1</span><br />- 1 ¼ hors<br />- 40 questions<br />- 40 marks<br /><br /><span style="font-weight: bold;">Paper 2</span><br />- 2 ½ hours<br />- working steps must be done<br />- Section A<br /> = 52 marks<br /> = 11 questions<br />- Section B<br /> = 48 marks<br /> = 5 questions (answer 4 of out 5)<br /><br />Every chapter will be tested in Paper 1. The questions will be tested from Form 1 until Form 5. Since you have already mastered the some basics in PMR, these shouldn’t be a problem. Do past year objective questions will strengthen your basic.<br /><br />In paper 2, there are only certain chapters that will be tested in SPM maths. That’s why I will concentrate more on paper 2. The whole paper 2 format based on past year questions in random order with brief tips below<br /><br /><span style="font-weight: bold;">Confirmed to be tested every year</span><br />Paper 2 (Section A)<br />1) Volume of solids (which was taught in form 2)<br /> - most of the formulae given are for this question<br /> - make sure the formulae are used correctly<br /> - combined solid is sum of volume of the solids<br /> - remaining solid is the subtraction of bigger solid and smaller solid<br /><br />2) Angles of elevation and depression<br /> -using trigonometry rule<br /><br />3) Mathematical reasoning<br /> - statement ‘and’ and ‘or’<br /> - If p, then q. If q, then p.<br /><br />4) Simultaneous linear equation<br /> - equalize the same unknown and take out<br /> Example : 4p - 2q = 15<br /> (2p + 4q = 19) x2 (times 2 to make unknown 4p same)<br /> - don’t use Add Math method, answers will be different.<br /><br />5) The straight line<br /> - y = mx + c<br /> - gradient, gradient….<br /> - What is c? c (y-intercept) is the point where the line touches the y-axis.<br /><br />6) Quadratic expressions and equations<br /> - ‘solve the equation’ is to find the unknown<br /> - change the equation of the question into this form<br /> - factorise by your own or using calculator<br /> - must state x = ?, x = ?, there will be 2 answers<br /><br />7) Matrices<br /> - will mostly ask inverse matrix<br /> - if you’re not sure about the answer, check if the whole outcome is identical to the inverse matrix in the question.<br />- the answer in a) is related to b) <br /><br />8) Area and perimeter of circles (same as number 1)<br /> - 2πr (perimeter or circumference) and πr2 (area)<br /> - (angle/360 degree) x the formulae above for the area or perimeter of certain part<br /><br />9) Probability<br /> - is more of (number / total number).<br /> - the formulae given are plain useless<br /> - final answer is never less than 0 or more than 1, 1 &gt; answer &gt; 0<br /><br />10) Gradient and area under a graph<br /> - based on speed/ time graph<br /> = distance is area of the graph<br /> = rate of change of velocity is gradient of the graph<br /> = speed is based on the graph (seldom being asked)<br /> - beware of total distance and total speed<br /><br /><span style="font-weight: bold;">Can be varied each year</span><br />1) Sets (2004 and 2006)<br /> - shading based on the questions (intersection or union)<br /> - beware of the complement such as A’<br /><br />2) Graph of functions (2005 and 2007)<br /> - the inequalities (upper line is &gt;, lower line is &lt;)<br /> - if slanted line, you can imagine it into horizontal straight line. Same concept as above.<br /><br />What’s the conclusion? 2008 will be ‘Sets’! Wow, I can predict what will come out in this year’s SPM. :D<br /><br />Paper 2 (Section B) Answer 4 questions<br />1) Graph of functions<br /> - Linear functions (less likely to come out as it’s a straight line after plotted)<br /> - Quadratic functions (2004 and 2005)<br /> - Cubic functions (2007)<br /> - Reciprocal functions (2006)<br /> = this question is easy because you can detect the type of graph after you plot it.<br /> = elastic ruler is recommended<br /> = x-axis and y-axis should be stated in the graph<br /><br />2) Transformation<br /> - Translation<br /> - Reflection<br /> - Rotation<br /> - Enlargement ( careful with the word ‘to’ and ‘from’ because it determines the image would be smaller or bigger)<br /> = combination of transformation like VT<br /> -do T before V. It's some kind of law.<br /><br />3) Statistic<br /> - Histogram ( 2004 and 2005)<br /> = x-axis the upper boundary with an additional lower boundary at the front of the graph<br /> = y-axis is frequency<br /> - Frequency Polygon (2006)<br /> = x-axis is midpoint<br /> = y-axis is frequency<br /> - Ogive (2007)<br /> = x-axis is upper boundary<br /> = y-axis is cumulative frequency<br /> = additional upper boundary should be added to the table<br /> = x-axis and y-axis should be stated in the graph<br /><br />My school hasn’t come to these chapters below, but I will try my best to explain it.<br />4) Plans and elevations<br /> -well I’m not sure but what I can see is you must be able to imagine the solid from every side<br /> -plan is looked from above<br /> -elevation is looked from the side of the solid<br /> -the length and the edge (ABCD) should be stated correctly<br /> -similar to a chapter of the living skills in PMR<br /><br />5) Earth as a sphere<br /> -no comment because I’m not going to explain something that I’m not sure<br /> -latitude is vertical and longitude is horizontal of the sphere<br /> -nautical mile<br /><br />If you concentrate on these chapters and do a lot of past year questions, I’m sure getting A1 in Maths is not a matter for you. Choose the 4 questions that you’re confident in section B paper 2. Do all questions if you think you have much time to spend for taking a nap. Why study more if you know what kind of questions will come out?<br /><br /><span style="font-weight: bold;">Additional Tips</span><br />1) You know doesn’t mean you can get correct, try to make less careless mistakes in each paper.<br />2) See through the questions word by word as there will be some tricky part in the questions, especially ‘to’ and ‘from’ in enlargement.<br />3) Don’t be sad if you do badly in trial SPM because the odd might come to you in SPM.<br />4) Be sure to study smart, not study hard. Hope this helps.</span>Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-36935602644115104362012-03-16T22:19:00.000-07:002012-03-16T22:19:14.119-07:00World Maths Day<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-CFVTgYuYDGU/T2QaCSEF_uI/AAAAAAAAAC4/7F3uMEXjTF0/s1600/wmd.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-CFVTgYuYDGU/T2QaCSEF_uI/AAAAAAAAAC4/7F3uMEXjTF0/s1600/wmd.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;">World Maths Day is an online international competition.In 2007,World Math Day was originally held on the March 14,and then on the 1st Wednesday in March subsequent years.Question sets come under five categories that is addition,subtraction,multiplication,division and simple equation.In each game,students has one minute to answer as many of these questions of a random category as they can.The level of difficulty is approximately age appropriate.Each age category have five level and each level consist of different kind of exercise.</div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Sg-HPWMe3B4/T2QaD0BWmQI/AAAAAAAAADA/DJ21mfqRZvQ/s1600/wmd2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Sg-HPWMe3B4/T2QaD0BWmQI/AAAAAAAAADA/DJ21mfqRZvQ/s1600/wmd2.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;">As you can see,math can bring nations together...</div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-64041881168663435182012-03-16T21:54:00.000-07:002012-03-16T21:54:42.902-07:00Algebra Equation is easy<div class="separator" style="clear: both; text-align: center;">Here's a simple algebra question.</div><div class="separator" style="clear: both; text-align: center;">Now lets find the value of "h" if 6h=18...</div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-cbVm0nhrJ_U/T2QWoRpzUCI/AAAAAAAAACo/CJQh3TlPSnk/s1600/solving+equation.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-cbVm0nhrJ_U/T2QWoRpzUCI/AAAAAAAAACo/CJQh3TlPSnk/s1600/solving+equation.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;">was't that easy.</div><div class="separator" style="clear: both; text-align: center;">Now let's find "k" if k/3=4</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-R2Pq9UYa1_c/T2QWt0-z8iI/AAAAAAAAACw/7Dv9FQAicVw/s1600/solving+equation2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-R2Pq9UYa1_c/T2QWt0-z8iI/AAAAAAAAACw/7Dv9FQAicVw/s1600/solving+equation2.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;">As you can see maths is very simple and easy,specially in Algebra Equation...</div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-34701571092876013182012-03-16T21:36:00.000-07:002012-03-16T21:40:58.408-07:00Math Joke<br />Joke 1:<br />The mother of already three is pregnant with her fourth child.<br />One evening, the eldest daughter says to her dad: "Do you know, daddy, what I've found out?"<br />"No."<br />"The new baby will be Chinese!"<br />"What?!"<br />"Yes. I've read in the paper that statistics shows that every fourth child born nowadays is Chinese..."<br /><br />Joke 2:<br />"What is Pi?"<br />A mathematician: "Pi is the ratio of the circumference of a circle to its diameter."<br />A computer programmer: "Pi is 3.141592653589 in double precision."<br />A physicist: "Pi is 3.14159 plus or minus 0.000005."<br />An engineer: "Pi is about 22/7."<br />A nutritionist: "Pie is a healthy and delicious dessert!"Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-71856863793890750072012-03-16T04:51:00.000-07:002012-03-16T04:53:52.881-07:00Volume Formulas<h3 style="color: cyan;"> <span style="font-family: Arial;">Note: "ab" means "a" multiplied by "b". "a<sup>2</sup>" means "a squared", which is the same as "a" times "a". "b<sup>3</sup>" means "b cubed", which is the same as "b" times "b" times "b".</span></h3><h3 style="color: cyan;"> <span style="font-family: Arial;">Be careful!! Units count. Use the same units for all measurements.&nbsp;</span></h3>cube = a<sup> 3</sup> <img align="bottom" src="http://www.math.com/tables/geometry/cube.gif" style="background-color: lime;" /> <br />rectangular prism = a b c <img align="bottom" src="http://www.math.com/tables/geometry/rprism.gif" style="background-color: lime;" /> <br />irregular prism = <b>b</b> h <img align="bottom" src="http://www.math.com/tables/geometry/prism.gif" style="background-color: lime;" /> <br />cylinder = <b>b</b> h = <i>pi</i> r<sup> 2</sup> h <img align="bottom" src="http://www.math.com/tables/geometry/cylinder.gif" style="background-color: lime; color: lime;" /> <br />pyramid = (1/3) <b>b</b> h <img align="bottom" src="http://www.math.com/tables/geometry/pyrimid.gif" style="background-color: lime;" /> <br />cone = (1/3) <b>b</b> h = 1/3 <i>pi</i> r<sup> 2</sup> h <img align="bottom" src="http://www.math.com/tables/geometry/cone.gif" style="background-color: lime;" /> <br />sphere = (4/3) <i>pi</i> r<sup> 3</sup> <img align="bottom" src="http://www.math.com/tables/geometry/circle.gif" style="background-color: lime;" /> <br />ellipsoid = (4/3) <i>pi</i> r<sub>1</sub> r<sub>2</sub> r<sub>3</sub> <img align="bottom" src="http://www.math.com/tables/geometry/ellipoid.gif" style="background-color: lime;" />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-49007981647884731372012-03-16T04:48:00.002-07:002012-03-16T04:48:37.998-07:00Math Problems?<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-pFgR5AqZWNw/T2MA5sWTK8I/AAAAAAAAACg/LntPtmE7Y5g/s1600/math_problems_call_1_800_14x_12i_2_sin_x_tshirt-p235407835097458072zvcav_400.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-pFgR5AqZWNw/T2MA5sWTK8I/AAAAAAAAACg/LntPtmE7Y5g/s320/math_problems_call_1_800_14x_12i_2_sin_x_tshirt-p235407835097458072zvcav_400.jpg" width="320" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-67975300435592623192012-03-16T01:57:00.001-07:002012-03-16T01:57:56.140-07:00The kind of face that we will see during math exam<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-zXLW4gTBnSQ/T2MAQr7ZMwI/AAAAAAAAACY/mD9LsA1PejA/s1600/math-problem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-zXLW4gTBnSQ/T2MAQr7ZMwI/AAAAAAAAACY/mD9LsA1PejA/s1600/math-problem.jpg" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0tag:blogger.com,1999:blog-1959024068493839817.post-41856329406553719762012-03-16T01:55:00.003-07:002012-03-16T01:55:38.399-07:00Math Questions<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-L5uNK3phnMs/T2L_uh8pTrI/AAAAAAAAACQ/0NnxCsVl7Po/s1600/Math_Questions2031.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="318" src="http://3.bp.blogspot.com/-L5uNK3phnMs/T2L_uh8pTrI/AAAAAAAAACQ/0NnxCsVl7Po/s320/Math_Questions2031.gif" width="320" /></a></div><br />Art_Troopershttp://www.blogger.com/profile/04598394268146044924noreply@blogger.com0